No, because this question doesn’t make sense (no offense intended, please see below).
No, the “target server” will have its own settings.
Guessing at your motivations, you also cannot get your “old” buildings/thralls etc back if transferring back to the original map (after a stint in the Exiled Lands), unless someone stayed behind “holding” those buildings/thralls for you in a clan (they’d then have to invite you back into said clan).
Since you’re on a private server, I believe it’s possible to set all this up for free via Family Sharing on Steam (if you’re on PC), I can’t say what options, if any, exist for consoles. In any case, that’s getting a bit off topic.
The answer is that there is no difference between a map transfer and a server transfer: any given server instance runs exactly one map (with one attached database). Transferring to another map is effectively (and practically) the exact same as transferring to another server instance, the only difference being that server instance running a different map.
All this applies whether the same physical machine runs multiple server instances/maps or not.
So a single server can have a single map loaded at one time. Your ultimate goal is achievable but will requires some steps.
backup the server before transfer and save it locally (to be used if you decide to go back to siptah)
Upload you characters.
Bring your server offline and change the map to Exiled lands.
Upload your character to your new server.
It’s a process that you wouldn’t want to do on a regular basis but if you are wanting to move your character from on map to the other for a long period of time that is how it could be done.
The other option would be to purchase a second server to run the other map on.
Something I experienced in a transfer is that all my food was gone. I’m thinking everything that can decay will disappear so I’m glad I didn’t take a named doggie with me. That would have been very disappointing.
Hey @Wak4863 just wanted to confirm one more thing.
This private server that my brother has can save data independently of map correct?
Let’s say for instance I have a level 60 character on exiled lands with 3 bases, when I switch the server to a Siptah map, then back to the exiled map, will I still have my level 60 character with 3 bases?